But going up and down multiplies expotentially the number of horizontal dimensions doesn't it? What are the odds that I'm going to be in exactly the same horizontal plane as another flying car?

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People not checking left of right before switching lanes accounts for about 4% of all accidents (US) and 0.5% of all deaths. Now, add not checking above or below you before switching altitudes and the number of deaths increases because you have to deal with crashing to Earth post wreck.

Distracted driving accounts for 17% of accidents and 10% of deaths. Make that distracted flying and the numbers go up. The airbag deployed, you're safe but the car was totaled out and is undrivable...now deal with plummeting from whatever altitude to the ground.

People not checking left of right before switching lanes accounts for about 4% of all accidents (US) and 0.5% of all deaths. Now, add not checking above or below you before switching altitudes and the number of deaths increases because you have to deal with crashing to Earth post wreck.

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The likelihood of you hitting another vehicle by changing altitude is immediately diminished by the unlikelihood that you will situate yourself on any given populated plane. I move 30 feet up. Or 36 feet up. What are the chances I've selected a populated plane of flight? Not much, considering the ratio of populated planes where another car happens to be located vs that of unpopulated planes where none are located at all.